Complete integrability of higher-dimensional Einstein equations with additional symmetry, and rotating black holes

TL;DR

This paper demonstrates how the Belinski-Zakharov method can be used to derive higher-dimensional black hole solutions, specifically the five-dimensional Myers-Perry metric, highlighting the integrability of Einstein equations with symmetry.

Contribution

It presents a new derivation of the five-dimensional Myers-Perry black-hole metric as a 2-soliton solution, illustrating the application of integrability methods to higher-dimensional Einstein equations.

Findings

Derivation of Myers-Perry metric as a 2-soliton solution

Application of Belinski-Zakharov method to higher-dimensional Einstein equations

Potential for analyzing black hole uniqueness in higher dimensions

Abstract

A new derivation of the five-dimensional Myers-Perry black-hole metric as a 2-soliton solution on a non-flat background is presented. It is intended to be an illustration of how the well-known Belinski-Zakharov method can be applied to find solutions of the Einstein equations in D-dimensional space-time with D-2 commuting Killing vectors using the complete integrability of this system. The method appears also to be promising for the analysis of the uniqueness questions for higher-dimensional black holes.